Basement Shower in Preparation for Full Bath Renovation

I am in the very early stages of planning for a renovation of my full bath on the second floor. To allow plenty of time to do the work

, I plan on setting up a temporary shower in the basement.

My question has two parts. First, I am curious to know if there are any questionable plumbing practices shown in the attached picture. Based on some screwy electrical things I've found, I wouldn't be surprised. So please take a close look and comment on what you see.

Please note that the vent in the top picture turns 90 degrees at the basement ceiling, crosses the basement, and connects to the stack in the middle and bottom pictures where I have indicated. Seems interesting, but I would like your thoughts.

Also, whoever added the half bath off the kitchen seems to have brought the vent shown down to the basement to connect to the existing vent. Is this okay?

The second question is this: what would be the best way to drain/vent a shower into the existing plumbing? I would like to use a Saniflo Sanishower or equivalent product to avoid any concrete smashing.

Please let me know if you have any questions or need any clarification.

FYI, I live in Erie, PA where we follow the 2003 International Plumbing Code, according to Erie's Uniform Construction Code.

That long "vent" CANNOT connect to ANYTHING in the basement. I has to connect to a vent riser at least 42" above the upstairs floor, or 6" above the overflow level of the upstairs fixtures if that would be HIGHER than 42". As it stands, there is also NO PLACE to "legally" connect a basement vent to the existing piping. And based on the picture, I cannot be sure that the piping I cannot see was done properly either.

So if I understand correctly, you are saying the laundry sink needs to be vented up to the second floor, 42" above the floor or 6" above the overflow level of the second floor bath sink most likely? I am sure this is what the code requires, but could you explain the practical reasons? To clarify, the second floor full bath is connected to the large waste stack near the dryer duct. The odd vent that leaves the laundry sink, crosses the basement just below the joists, and connects on the other side of the basement (2nd and 3rd pictures), doesn't connect to the second floor bath pipes again. It meets up with another vent that goes up through the kitchen, second floor, attic, and roof. I would imagine/hope that the kitchen sink would be vented into this vertical vent pipe higher than the sink, but who knows.

As for the bathroom addition, there are two pipes coming from it. I am guessing the smaller one is supposed to serve as a vent. If true, this vent cannot attach in the basement, correct, even if it were to rise 42" above the floor first before dropping down?

These may be stupid questions, but there's a lot of odd past DIY work to figure out in this house. I once found one switch of a 4-way circuit--still functioning--buried inside my kitchen wall. I just wish people would think about the things they do before they do them. I like to learn how to do things correctly, so this forum at least gets me pointed in the right direction to do my research.